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polet [3.4K]
2 years ago
8

Prove the identity.cosx sin (x+y) - sinx cos(x+y) = siny​

Mathematics
1 answer:
Jet001 [13]2 years ago
6 0

Answer:

In the explanation

Step-by-step explanation:

Going to start with the sum identities

sin(x+y)=sin(x)cos(y)+sin(y)cos(x)

cos(x+y)=cos(x)cos(y)-sin(x)sin(y)

sin(x)cos(x+y)=sin(x)cos(x)cos(y)-sin(x)sin(x)sin(y)

cos(x)sin(x+y)=cos(x)sin(x)cos(y)+cos(x)sin(y)cos(x)

Now we are going to take the line there and subtract the line before it from it.

I do also notice that column 1 have cos(y)cos(x)sin(x) in common while column 2 has sin(y) in common.

cos(x)sin(x+y)-sin(x)cos(x+y)

=0+sin(y)[cos^2(x)+sin^2(x)]

=sin(y)(1)

=sin(y)

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Find the missing angles in the following triangles.
Bezzdna [24]

Answer:

Step-by-step explanation:

angles in triangle = 180

1. 180 - (70+45) = x = 65

2. x = 35

180 - 110 = 70

70/2 = 35 (isosceles triangle)

3. x = 113, y = 67

180 - (62 + 51) = y = 67

Angles on a line = 180

180 - 67 = x = 113

4. x = 60, y = 50

x = 180 - 120 = 60

y = 180 - (60 + 70) = 50

answers in degrees.

8 0
2 years ago
Jenny’s mom gave her one dollar on the day she was born. She plans to triple the amount she gives her every day. How much will s
astraxan [27]

Answer:

19,683

Step-by-step explanation:

3 0
3 years ago
Can someone help me ?
Kisachek [45]
D is your answer

1/3 of 18 is 6, so 2/3 would be 12
8 0
2 years ago
How do I solve 1/2z=9 1/4?
Nastasia [14]

Answer:

z = 9/2

Step-by-step explanation:

1/2z = 9 1/4?

z = 9/2

Explanation:

Simplify

9 x 1/4 → 9/4

Multiply 2 to both sides to cancel out the 2

1z = 9/4

Note: 1z is just z

6 0
3 years ago
If 3,x,y,18 are in arithmetric progression , find the value of x and y
Ksivusya [100]
Given:
arithmetic progression
a₁ = 3
a₂ = x
a₃ = y
a₄ = 18

Solution:
The arithmetic progression has general formula to determine nth term
a₁ + d(n - 1) = an
a₁ represents first term, d represents difference, n represents number of terms, an represents nth term

First we should find out the value of d, by submitting a₄ to the formula
a₁ + d(n - 1) = an
a₁ + d(4 - 1) = a₄
3 + d(3) = 18
3 + 3d = 18
3d = 15
d = 5
The difference of the sequence is 5

Second, determine x and y
x = a₂
x = a₁ + d(2 - 1)
x = 3 + 5(1)
x = 8

y = a₃
y = a₁ + d(3 - 1)
y = 3 + 5(2)
y = 13

The value of x is 8, the value of y is 13
6 0
3 years ago
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